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QQuanta KidsBy IIT & ISB Alumni
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Concept 3 of 5

Counting the Ways

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Today's big idea

List them, then count

Be orderly so you miss none.

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How it works

👀 What's going on?

How many outfits can you make from two shirts and two pairs of shorts? Rather than guess, you can list every pairing and count — and never miss one.

💡 Here's the trick

Count every way it can happen3 ways

Look at the problem above. To count how many ways something can happen, list the possibilities in an orderly way and count them, or match each choice on one side with every choice on the other.

  1. 1.Decide what each way looks like.
  2. 2.List them in order so none is missed or repeated.
  3. 3.Count how many you listed.

✍️ Try it

How many 2-digit numbers can you make from 1, 2 and 3 without repeating a digit? List them: 12, 13, 21, 23, 31, 32. That is 6 numbers.

⚠️ Watch out

Be orderly, or you will double-count or miss one. Going 12, 13, then 21, 23, then 31, 32 keeps every number once.

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See it in action

⚡ Time to play!

Count carefully — list every possibility so you do not miss one or repeat one.

COUNT THE WAYS · ROUND 1 OF 3

How many different 2-digit numbers can you make from the digits 1, 2 and 3 without repeating a digit?

How many ways are there?

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Quick check

✅ VERIFICATION

You have 3 caps and 1 scarf. How many cap-and-scarf sets can you make?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Calendar Logic

Dates 7 apart share a day.

Concept 4 of 5